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Theses

Etude asymptotique des algorithmes stochastiques et calcul des prix des options Parisiennes

Abstract : The first part of this thesis is devoted to the study randomly truncated stochastic algorithms as introduced by Chen and Zhu. The first study is concerned with the almost sure convergence. We continue the study with the convergence rate of the algorithm. We also consider a moving window version of the algorithm. Finally, we present a few applications to finance.
The second part of the thesis is concerned with the pricing of Parisian options. The valuation technique is based on computing closed form formula for the Laplace transforms of the prices following the seminar work of Chesney, Jeanblanc and Yor on the topic. We determine
these formulae for the single and double barrier Parisian options. Then, prove the accuracy of the numerical inversion methods we use ton invert these Laplace transforms.
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https://tel.archives-ouvertes.fr/tel-00201373
Contributor : Jérôme Lelong <>
Submitted on : Friday, December 28, 2007 - 12:45:37 PM
Last modification on : Tuesday, April 24, 2018 - 1:32:45 PM
Long-term archiving on: : Tuesday, April 13, 2010 - 3:47:28 PM

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Jérôme Lelong. Etude asymptotique des algorithmes stochastiques et calcul des prix des options Parisiennes. Mathématiques [math]. Ecole Nationale des Ponts et Chaussées, 2007. Français. ⟨tel-00201373⟩

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